We propose a flexible regression model to study the association between a functional response and multiple functional covariates that are observed on the same domain. Specifically, we relate the mean of the current response to current values of the covariates by a sum of smooth unknown bivariate functions, where each of the functions depends on the current value of the covariate and the time point itself. In this framework, we develop estimation methodology that accommodates realistic scenarios where the covariates are sampled with or without error on a sparse and irregular design, and prediction that accounts for unknown model correlation structure. We also discuss the problem of testing the null hypothesis that the covariate has no association with the response. The proposed methods are evaluated numerically through simulations and two real data applications.

中文翻译：

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加性非线性泛函并发模型

我们提出了一个灵活的回归模型来研究功能响应与在同一域上观察到的多个功能协变量之间的关联。具体来说，我们将当前响应的平均值与协变量的当前值相关联，通过平滑的未知双变量函数的总和，其中每个函数都取决于协变量的当前值和时间点本身。在此框架中，我们开发了一种估计方法，该方法适用于在稀疏和不规则设计中对协变量进行有误或无误采样的现实场景，以及对未知模型相关结构进行预测的预测。我们还讨论了检验协变量与响应没有关联的零假设的问题。